Bookmakers rate of return?

Question by Wonhi: Bookmakers rate of return?
The formula for calculating a bookmakers rate of return is to take the inverse of the sum of all outcomes. Why is this the case? I'm trying to understand this intuitively but can't seem to wrap my head around it. If anyone can explain I would appreciate it.

For reference, I came across the formula here http://en.wikipedia.org/wiki/Arbitrage_betting. Just search for the section "Arbitrage using bookmakers".


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